from a handpicked tutor in LIVE 1-to-1 classes

# If an equation of the linear function is y = mx + b, then what is m?

Straight lines are very important concepts in mathematics which are represented by linear equations in a cartesian plane. They have a constant slope.

## Answer: If an equation of the linear function is y = mx + b, then m is the slope of the line.

Let's understand the solution in detail.

**Explanation:**

The equation y = mx + b is a linear equation; hence it represents a straight line. Any point (x_{1}, y_{1}) on this line must satisfy this equation as

⇒ y_{1} = mx_{1} + b ---------- (1)

Now let's take a random point P(x_{2}, y_{2}) on the given line. Now we have:

⇒ y_{2 }= mx_{2} + b ---------- (2)

Now if we find equation (2) - (1), we get y_{2} - y_{1} = m (x_{2} - x_{1})

Hence, m = (y_{2} - y_{1}) / (x_{2} - x_{1})

This formula denotes the change in the vertical coordinates divided by the change in the horizontal coordinates which is the definition for slope.

### Hence, if an equation of the linear function is y = mx + b, then m is the slope of the line.

visual curriculum